ECE 8830 Electric Drives

1
ECE 8830 - Electric Drives
Topic 15 Permanent Magnet Synchronous
and Variable Reluctance Motors
Spring 2004
2
Introduction

• Permanent magnet synchronous motors have the
  rotor winding replaced by permanent magnets.
  These motors have several advantages over
  synchronous motors with rotor field windings,
  including
• Elimination of copper loss
• Higher power density and efficiency
• Lower rotor inertia
• Larger airgaps possible because of larger
  coercive force densities.

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Introduction (contd)

• Some disadvantages of the permanent magnet
  synchronous motor are
• Loss of flexibility of field flux control
• Cost of high flux density permanent magnets is
  high
• Magnetic characteristics change with time
• Loss of magnetization above Curie temperature

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Permanent Magnets

• Advances in permanent magnetic materials over
  the last several years have had a dramatic impact
  on electric machines. Permanent magnet materials
  have special characteristics which must be taken
  into account in machine design. For example, the
  highest performance permanent magnets are brittle
  ceramics, some have chemical sensitivities, all
  have temperature sensitivity, and most have
  sensitivity to demagnetizing fields. Proper
  machine design requires understanding the
  materials well.

5
B-H Loop

• A typical B-H loop for a permanent magnet is
  shown below. The portion of the curve in which
  permanent magnets are designed to operate in
  motors is the top left quadrant. This segment is
  referred to as the demagnetizing curve and is
  shown on the next slide.

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Demagnetizing Curve

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Demagnetizing Curve (contd)

• The remnant flux density Br will be available
  if the magnet is short-circuited. However, with
  an air gap there will be some demagnetization
  resulting in the no-load operating point, B.
  Slope of no-load line is smaller with a larger
  air gap. With current flowing in the stator,
  there is further demagnetization of the permanent
  magnet causing the operating point to shift to C
  at full load.

8
Demagnetizing Curve (contd)

• Transients or machine faults can lead to a
  worst-case demagnetization as shown which results
  in permanent demagnetization of the permanent
  magnet. The recoil line following the transient
  is shown and shows a reduced flux density
  compared to the original line. It is clearly
  important to control the operation of the magnets
  to keep the operating point away from this
  worst-case demagnetization condition.

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Permanent Magnetic Materials

• Alnico - good properties but too low a coercive
  force and too square a B-H loop gt permanent
  demagnetization occurs easily
• Ferrites (Barium and Strontium) - low cost,
  moderately high service temperature (400?C), and
  straight line demagnetization curve. However, Br
  is low gt machine volume and size needs to be
  large.

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Permanent Magnet Materials (contd)

• Samarium-Cobalt (Sm-Co) - very good properties
  but very expensive (because Samarium is rare)
• Neodymium-Iron-Boron (Nd-Fe-B) - very good
  properties except the Curie temperature is only
  150?C

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Permanent Magnet Materials (contd)

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PM Motor Construction

• There are two types of permanent magnet motor
  structures
• 1) Surface PM machines
• - sinusoidal and trapezoidal
• 2) Interior PM machines
• - regular and transverse

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Circuit Model of PM Motor (contd)

• Based on the recoil line, we can write
• where Prc, the permeance, is the slope of
• the line. From this equation we can write

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Equivalent Circuit Model of PM Motor

• Rearranging the slope equation, we get
• This equation suggests the following equivalent
  circuit for a permanent magnet

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Equivalent Circuit Model of PM Motor (contd)

• It can be shown that the mmf, flux and
  permeance are the mathematical duals of current,
  voltage, and inductance, respectively. Therefore,
  the following electrical equivalent circuits can
  be used to represent the magnetic circuit

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Equivalent Circuit Model of PM Motor (contd)

• We can now use this equivalent circuit of the
  permanent magnets on the rotor and the previous
  equivalent equivalent circuits of the synchronous
  motor to develop a set of qd0 equivalent circuits
  for the permanent magnet synchronous motor.
  Assuming the PM synchronous motor has damper cage
  windings but no g winding, the qd0 equivalent
  circuits are as shown on the next slide.

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Equivalent Circuit Model of PM Motor (contd)

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Equivalent Circuit Model of PM Motor (contd)

• Here the PM magnet inductance Lrc can be
  lumped with the common d-axis mutual inductance
  of the stator and damper windings, and the
  combined d-axis mutual inductance indicated by
  Lmd. Also, the current im is the equivalent
  magnetizing current for the permanent magnet
  referred to the stator side.

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qd0 Equations for Permanent Magnet Synchronous
Motor

• The qd0 equations for a permanent magnet motor
  are given in the table below

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qd0 Equations for Permanent Magnet Synchronous
Motor (contd)

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qd0 Equations for Permanent Magnet Synchronous
Motor (contd)

• The developed electromagnetic torque expression
  has three components
• 1) A reluctance component (which is negative
  for LdltLq)
• 2) An induction component (which is asynchronous
  torque)
• 3) An excitation component from the field of the
  permanent magnet.

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qd0 Equations for Permanent Magnet Synchronous
Motor (contd)

• The mutual flux linkages in the q- and
  d-axes may be expressed by
• The winding currents can be expressed (as
  before) as

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qd0 Equations for Permanent Magnet Synchronous
Motor (contd)

• Combining these equations gives
• where .
• Similar expressions for ?mq and LMQ can be
  written for the q-axis.

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qd0 Equations for Permanent Magnet Synchronous
Motor (contd)

• Under steady state conditions where ??e as in
  the case of Ef in the wound field synchronous
  motor, we can express ?e?m or xmdim by Em, the
  permanent magnets excitation voltage on the
  stator side. If the stator resistance is
  neglected and the Ef term in the earlier torque
  expression replaced by Em, the torque of a
  permanent magnet synchronous motor in terms of
  the rms phase voltage Va at its terminal can be
  written as

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Simulation of PM Synchronous Motor

• A line-start permanent magnet motor has
  magnets embedded in the rotor to provide
  synchronous excitation and a rotor cage provides
  induction motor torque for starting. Thus it is
  a high efficiency synchronous motor with
  self-start capability when operated from a fixed
  frequency voltage source.

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Simulation of PM Synchronous Motor (contd)

• The simulation equations for the PM synchronous
  motor are given below

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

• The Simulink file s4 in Ch.7 Ong implements a
  simulation of a line-start 3? PM synchronous
  motor connected directly to a 60Hz, 3? supply of
  rated voltage. The overall block diagram is

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Simulation of PM Synchronous Motor (contd)

• This slide and the next few slides show the
  internal blocks of the Simulink model.

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

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Simulation of PM Synchronous Motor (contd)

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Trapezoidal Surface Magnet Motor

• A trapezoidal surface permanent magnet motor
  is the same as a sinusoidal PM motor except the
  3? winding has a concentrated full-pitch
  distribution instead of a sinusoidal
  distribution.

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Trapezoidal Surface Magnet Motor (contd)

• This 2-pole motor has a gap in the rotor
  magnets to reduce flux fringing effects and the
  stator has 4 slots per phase winding per pole. As
  the machine rotates the flux linkage will vary
  linearly except when the magnet gap passes
  through the phase axis. If the machine is driven
  by a prime mover, the stator phase voltages will
  have a trapezoidal wave shape as shown on the
  next slide.

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Trapezoidal Surface Magnet Motor (contd)

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Trapezoidal Surface Magnet Motor (contd)

• An electronic inverter is required to
  establish a six-step current wave to generate
  torque. With the help of an inverter and an
  absolute-position sensor mounted on the shaft,
  both sinusoidal and trapezoidal SPM motors can
  serve as brushless dc motors (although the
  trapezoidal SPM motor gives closer dc
  machine-like performance).

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Synchronous Reluctance Motor

• A synchronous reluctance motor has the same
  structure as that of a salient pole synchronous
  motor except that it does not have a field
  winding on the rotor.

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Synchronous Reluctance Motor (contd)

• The stator has a 3?, symmetrical winding which
  creates a sinusoidal rotating field in the air
  gap. This causes a reluctance torque to be
  created on the rotor because the magnetic field
  induced in the rotor causes it to align with the
  stator field in a minimum reluctance position.
  The torque developed in this type of motor can be
  expressed as

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Synchronous Reluctance Motor (contd)

• The reluctance torque stability limit can be
  seen to occur at (see figure below).

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Synchronous Reluctance Motor (contd)

• Iron laminations separated by non-magnetic
  materials increases reluctance flux in the
  qe-axis. With proper design, the reluctance motor
  performance can approach that of an induction
  motor, although it is slightly heavier and has a
  lower power factor. Their low cost and robustness
  has seen them increasingly used for low power
  applications, such as in fiber-spinning mills.

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Variable Reluctance Motors

• A variable reluctance motor has double
  saliency, i.e. both the rotor and stator have
  saliency. There are two groups of variable
  reluctance motors stepper motors and switched
  reluctance motors. Stepper motors are not
  suitable for variable speed drives.

Ref A. Hughes, Electric Motors and Drives,
2nd. Edn. Newnes
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Switched Reluctance Motors

• The structure of a switched reluctance motor is
  shown below. This is a 4-phase machine with 4
  stator-pole pairs and 3 rotor-pole pairs (8/6
  motor). The rotor has neither windings nor
  permanent magnets.

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Switched Reluctance Motors (contd)

• The stator poles have concentrated winding
  rather than sinusoidal winding. Each stator-pole
  pair winding is excited by a converter phase,
  until the corresponding rotor pole-pair is
  aligned and is then de-energized. The stator-pole
  pairs are sequentially excited using a rotor
  position encoder for timing.

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Switched Reluctance Motors (contd)

• The inductance of a stator-pole pair and
  corresponding phase currents as a function of
  angular position is shown below.

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Switched Reluctance Motors (contd)

• Applying the stator pulse when the inductance
  profile has positive slope induces forward
  motoring torque.
• Applying the stator pulse during the time that
  the inductance profile has negative slope induces
  regenerative braking torque.
• A single phase is excited every 60? with four
  consecutive phases excited at 15? intervals.

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Switched Reluctance Motors (contd)

• The torque is given by
• where minductance slope and
• iinstantaneous current.

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Switched Reluctance Motors (contd)

• Switched reluctance motors are growing in
  popularity because of their simple design and
  robustness of construction. They also offer the
  advantages of only having to provide positive
  currents, simplifying the inverter design. Also,
  shoot-through faults are not an issue because
  each of the main switching devices is connected
  in series with a motor winding. However, the
  drawbacks of this type of motor are the pulsating
  nature of their torque and they can be
  acoustically noisy (although improved mechanical
  design has mitigated this problem.)